## Divisibility Rules: How to Improve at DILR & QA

Learn Divisibility rules to score better in DILR & QA. This guide serves as an easy memory-refresher for every time you need to revise Divisibility rules.

Divisibility Rules are important to save time in the CAT exam. Yes, you read it right. Divisibility rules that we had learnt in middle school are critical to prepare for an MBA entrance exam.

How do they save us time?

Firstly, they make your calculations faster in the DILR (Data Interpretation and Logical Reasoning). Secondly, in the Quantitative Aptitude Section, Divisibility Rules are used to solve many questions based on Number Theory.

So, there. That’s why you should learn Divisibility Rules.

## Divisibility Rules: 1 to 20

### Rule for 1

It is a mathematical fact that 1 is a factor for every number that could ever exist. So, 1 is divisible by every number.

### Rule for 2

For a number to be divisible by 2, it should have an even number in its ones place.

Example:

32 is divisible by 2 because it has 2 in its ones place.

78 is divisible by 2 because it has 8 in its ones place.

### Rule for 3

The sum of the digits must be a multiple of 3. Then, It will be divisible by 3.

Example:

71 is not divisible by three, since the sum of its digits is 8. 8 is not a multiple of 3. Therefore, 71 is not divisible by 3.

51 is divisible by three, since the sum of its digits is 6. 6 is a multiple of 3. Therefore, 51 is divisible by 3.

### Rule for 4

There are three ways to find if a number is divisible by 4.

(i) The last two digits of the number must be a multiple of 4

(ii) The ones place must have 0, 4, or 8 if the tens digit is even. However, If the tens digit is odd, the ones digit must have 2 or 6.

(iii) Double the tens digit of the number and add the ones digit to the product. Then, check if the resultant number is a multiple of 4 or not.

Tip: Use the third method for numbers with more 4-digits.

Example:

832 is divisible by 4. Can you say why?

### Rule for 5

The last digits of the number must be 0 or 5. Then, the number is divisible by 5.

Example:

90 is divisible by 5 because the last digit is 0.

### Rule for 6

The number must be divisible by 2 and 3.

Example:

1458 is divisible by 6. It has an even number in its ones place. It is divisible by 3 because the sum of the digits of the number is a multiple of 3.

### Rule for 7

If a number is divisible by 7, then on subtracting twice the digit in ones place from the rest of the number must either result in a multiple of 7 or 0.

Example:

749 is divisible by 7 because 74 – 18 = 56. Thus, 56 is a multiple of 7. It is divisible by 7.

### Rule for 8

There are multiple rules to verify whether a number is divisible by 8. Here, we’ll be discussing the two given below.

(i) Separate the last digit from the rest of the number, then, double the rest of the number. Now, add the last digit to it. The resultant must be a multiple of 8.

(ii) The last three digits of the number must be divisible by 8.

Tip: For numbers with more than 3-digits, first use the second method and then, apply the first method to those last three digits.

Example:

34,152

Consider the last three digits: 152

Now, separate the last digit from the rest of the number.

Double the remaining number: 15 × 2 = 30

Then, add the last digit to the product: 30 + 2 = 32;

We know that 32 is a multiple of 8 (8 × 4 = 32)

Therefore, 34,152 is divisible by 8

### Rule for 9

The sum of all the digits of the number must be a multiple of 9. Then, it will be divisible by 9.

Example:

2889: 2 + 8 + 8 + 9 = 27

We know that 9 × 3 = 27

Therefore, 2889 is divisible by 9

### Rule for 10

The digit in the ones place must be 0 for the given number to be divisible by 10.

Example:

88800 is divisible by 10 because it has 0 in its ones place.

### Rule for 11

The difference between the sum of the digits in the even places and the sum of the digits in the odd places must be a multiple of 11 or 0.

Example:

918,082

Sum of the digits in the odd places: 2 + 0 + 1 = 3

Sum of the digits in the even places: 8 + 8 + 9 = 25

The difference between the two sets of sums: 25 – 3 = 22

We know that, 11 × 2 = 22

Therefore, 918,082 is divisible by 11.

### Rule for 12

There are two ways to know if a number is divisible by 12:
(i) It must be divisible by 3 and 4.
(ii) On subtracting the last digit of the number from twice the remaining number, the resultant must be a multiple of 12.

Example:

972:

9 + 7 + 2 = 18

It is divisible by 3

(7 × 2) + 2 = 16

The resultant is a multiple of 4. So, it is divisible by 4.

Therefore, 972 is divisible by 12 because the number is divisible by 3 and 4.

### Rule for 13

On adding four times the digit in the units place to the rest, the resultant must be a multiple of 13.

Example:

923 :

92 + (3 × 4) = 104

⇒ 10 + (4 × 4) = 26

26 is a multiple of 13 because 13 × 2 = 26.

Therefore, 923 is divisible by 13.

### Rule for 14

There are two ways to verify the divisibility of a number by 14.

(i) The number must be divisible by 7 and 2.

(ii) On adding the last two digits to twice the rest of the number, the resultant obtained must be a multiple of 14.

Example:

224:

(2 × 2) + 24 = 28

We know that,  14 × 2 = 28

So, the given number is divisible by 14.

### Rule for 15

The given number must be divisible by 3 and 5

Example:

405

4 + 0 + 5 = 9

Hence, the given number is divisible by 3

The last digit of the number is 5. So, it is divisible by 5.

Therefore, the given number is divisible by 15 as it is divisible by 3 and 5.

### Rule for 16

For a number to be divisible by 16, the resultant obtained when adding the last two digits to four times the rest of the number must be a multiple of 16.

Example:

1184

(11 × 4) + 84 = 44 + 84

⇒ 128

(1 × 4) + 28 = 4 + 28

⇒ 32

As the product of 16 and 2 is equal to 32, the given number is divisible by 16.

### Rule for 17

The difference between the last two digits and two times the remaining number must be a multiple of 17 to be divisible by 17.

Example:

4,675

(46 × 2) – 75 = 17

We know that 17 is a multiple of itself. Therefore, the given number is divisible by 17.

### Rule for 18

The number must be divisible by 9 and 2. Then, it is divisible by 18

Example:

342

The last digit is even. So, it is divisible by 2.

3 + 4 + 2 = 9

As 9 is a multiple of itself, the number is divisible by 9.

Therefore, the given number is divisible by 18.

### Rule for 19

On addition of twice the last digits to the rest of the number, the resultant must be a multiple of 19.

Example:

437:

43 + (7 × 2) = 57

So, we know that thrice 19 is 57. Therefore, the number is divisible by 19.

### Rule for 20

The given number must be divisible by 10 or have 0 in its units place, and it should have an even number in the tens place for the number to be divisible by 20.

Example:

460

The units place has 0. So, it is divisible by 10.

The number has an even number in its tens place, that is, 6. So, it satisfies both the conditions of divisibility by 20.

Therefore, the given number is divisible by 20.

I hope you find this useful!

If you have any doubts, just drop them in the comments section below or email our CAT coaching Kolkata at bellingthecat2@gmail.com

Happy learning!